Adam starts with the number z=1+2i on the complex plane. First, he dilates z by factor of 2 about the origin. Then, he reflects it across the real axi

Adam starts with complex number Z=1+2i
After getting dilated by a factor of 2 , Z becomes 2+4i
Then the number is reflected across the real axis, so the number becomes 2-4i
Now, the resulting number is rotated ${\displaystyle {90}^{\circ }}$ anticlockwise .
we know if point (a, b) is rotated anticlockwise by the angle α, then we get point ${\displaystyle (a\cos \alpha -b\sin \alpha ,b\cos \alpha +a\sin \alpha )}$ so (2,-4) after gets rotated 90°anticlockwise becomes ${\displaystyle (2{\cos 90}^{\circ }+4{\sin 90}^{\circ },-4{\cos 90}^{\circ }+2{\sin 90}^{\circ })=(4,2).}$
So, the resulting complex number is 4+2i